We humans have a significant ability to create using our fantasy. Was this ability given to us by God, a Creator as He created man in His image, according to His likeness, or was this ability developed itself while world became more complex?

@Flimzy: Not one of those links constitute any reasonable form of art; by that standard, I am an artist with paint and canvas, which I can assure you I am not. Show me a chimp painting a landscape and we can discuss the artistic ability of animals.
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Lawrence DolSep 30 '11 at 2:17

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@SoftwareMonkey: I can't even show you a 3 year old human who can paint a believable landscape... but I don't think that means a drawing of a 3-year-old is not creative... or "art."
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FlimzySep 30 '11 at 2:19

There is a quote on this that I love, from Alexander "Greek" Thomson, a 19th century Scottish Architect.

Some say that man can never get beyond his experiences. Whence then come Music and Architecture? There is nothing in Nature like either......they are something that by man or through his agency has been added to the work of God, and that, not presumptuously or sinfully, but by destiny and beauty; for being made in the image of God, man was made partaker of the divine nature so far as to become a fellow-worker with God - in however a humble a sense, a co-Creator.

Just one man's opinion, and a quite eccentric man at that. As you can see in questions like this, there is no real consensus on exactly what being in the image of God means, but I think it is very significant that the first time the Bible mentions people being filled with the Holy Spirit it is in order to carry out the creative work of building the tabernacle:

Then Moses said to the Israelites, “See, the Lord has chosen Bezalel son of Uri, the son of Hur, of the tribe of Judah, and he has filled him with the Spirit of God, with wisdom, with understanding, with knowledge and with all kinds of skills — to make artistic designs for work in gold, silver and bronze, to cut and set stones, to work in wood and to engage in all kinds of artistic crafts. And he has given both him and Oholiab son of Ahisamak, of the tribe of Dan, the ability to teach others. He has filled them with skill to do all kinds of work as engravers, designers, embroiderers in blue, purple and scarlet yarn and fine linen, and weavers—all of them skilled workers and designers. (Exodus 35:30-35)